Does the Web Dispatcher change the host header?
No. SAP systems support name-based virtual hosting. For this to work, the Host header must not be changed by the intermediary. As a matter of fact, if you use Apache as an intermediary in front of an SAP Application Server, you must configure "ProxyPreserveHost On" to prevent Host header modification.
If you really must modify the Host header, for example, to satisfy an EXTSERV external system, you can use the Web Dispatcher's rewrite handler to manipulate header fields.